赋权图过指定点的圈

Large cycles passing through a specified vertex in weighted graphs

设G是满足条件D1和D2的2-连通非Hamilton赋权图,证明了如下新结果:若G满足dw(x)+dw(y)≥m(xy E(G),x≠y),则通过图G的每个顶点存在权重大于或等于m的圈.该结果推广了非赋权图的已有结果.

Under the assumption that G is a 2-connected non-Hamilton weighted graph satisfying conditions D1 and D2, a new conclusion is verified： if G satisfies d^w（ x ） ＋ d^w（ y ） ≥ m（ xy 不属于 E（G）, x ≠ y ）, through each vertex of graph G, there exist cycles with the weight equal to or greater than m. The conclusion extends Enomoto＇ s theorem for the unweighted graphs to the weighted graphs.